Green Card Holders
Every year almost half a million people obtain Green Cards. When you become a Green Card holder, you are under the same obligations to file US tax returns as US citizens (ie see www.taxesforexpats.com/expat-tax-advice/why-file.html). We help hundreds of clients who are Green Card holders and continue to live outside the US.
Only then will the tax-related obligations come to an end. Noncompliance with tax obligations may give rise to high penalties - the same as for US citizens.